x³+2x²+2x+1=(x³+1)+(2x²+2x)=(x+1)(x²-x+1)+2x(x+1)=(x+1)(x²+x+1)=(x+1)[(x²+x+1/4)+3/4]=(x+1)[(x+1/2)²+3/4][]内恒大于零,所以方程有一个实数根x=-1,一对复数根x=(1±i...